Could someone please explain to me clearly how to work this out using quadratics? Find the values of a, b, c, d and e that make this following equation true. 4x^(2)(x-2)(x+3)+3 …

Question

Could someone please explain to me clearly how to work this out using quadratics?

Find the values of a, b, c, d and e that make this following equation true.
4
`x^(2)`(x-2)(x+3)+3 = ax
`x^(4)`+b
`x^(3)`+c
`x^(2)`+dx+e

Answer 1

`4x^2(x-2)(x+3)+3=ax^4+bx^3+cx^2+dx+e\\ 4x^2(x^2+3x-2x-6)+3=ax^4+bx^3+cx^2+dx+e\\ 4x^2(x^2+x-6)+3=ax^4+bx^3+cx^2+dx+e\\ 4x^4+4x^3-24x^2+3=ax^4+bx^3+cx^2+dx+e\\\\ a=4\\ b=4\\ c=-24\\ d=0\\ e=3`